# NSVB Douglas-fir, Tropical Subtropical Steppe Regime Mountains (M310): total stem wood volume (inside bark), segmented model (Eq. 2), D < 9 in (22.86 cm)

Stem volume equation for Pseudotsuga menziesii, United States, from Westfall et al. 2024. 339 trees, DBH 2.54–22.86 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Westfall et al. 2024 (Table S1a (Table S1a_volib_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1):

> 202,M310,,2,0.004126027,,1.688585292,1.92854407,0.982841682,

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#equation

In this library's units, ready to compute (stem volume in m³):

```
Stem volume = 0.028316846592 * 0.004126027 * (D/2.54)^1.688585292 * (H/0.3048)^0.982841682
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.004126027 * DBH^1.688585292 * HT^0.982841682, with DBH in in, HT in ft; output in ft3.
Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: Pseudotsuga menziesii (species), family Pinaceae; conifer
- Where: FIA ecodivision Tropical Subtropical Steppe Regime Mountains (M310), mapped in GTR fig. 1. Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#where
- Biomes: subtropical, dryland, montane
- Stand: not stated
- Trees measured: 339. Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#n_trees
- DBH range: 2.54–22.86 cm. Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#dbh
- Method: NSVB segmented model (Eq. 2), coefficients for SPCD 202 in DIVISION M310 from table S1a; fitted with weighted regression to destructively sampled trees. Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#checked_at

A missing fit statistic is one the source doesn't state, or that we haven't recorded; it is never estimated. Outside the stated DBH range or region, the equation is an extrapolation.

## Source

Westfall, J.A., Coulston, J.W., Gray, A.N., Shaw, J.D., Radtke, P.J., Walker, D.M., Weiskittel, A.R., et al. (2024). A national-scale tree volume, biomass, and carbon modeling system for the United States. Gen. Tech. Rep. WO-104. Washington, DC: USDA Forest Service. 37 p.

- DOI: https://doi.org/10.2737/WO-GTR-104
- Access: open access
- Copy we read: https://research.fs.usda.gov/download/treesearch/66998.pdf
- Every equation from this source: https://treeallometry.org/sources/westfall-2024/
- Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#source

## The facts, in the source's words

**Equation** (Table S1a (Table S1a_volib_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1):

> 202,M310,,2,0.004126027,,1.688585292,1.92854407,0.982841682,

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#equation

**Equation** (Eq. 2, p. 2):

> yi = a × Di^b × Hi^c + εi; Di < k / yi = a × k^(b−b1) × Di^b1 × Hi^c + εi; Di ≥ k

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-expression

**Units** (Methods, Model development, p. 2):

> Di is diameter (inches) at breast height (4.5 feet), Hi is total tree height (feet)

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-published-units

**published.output unit** (Examples of tree-level calculations, p. 8):

> units for volume and biomass predictions are cubic feet and pounds, respectively

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-published-output-unit

**Taxon** (FIADB REF_SPECIES.csv (FIA DataMart), columns SPCD,COMMON_NAME,SHARED_COMMON_NAME_IND,GENUS,SPECIES,VARIETY,SUBSPECIES,SCIENTIFIC_NAME: the species codes the NSVB tables use):

> 202,Douglas-fir,N,Pseudotsuga,menziesii,,,Pseudotsuga menziesii

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-taxon

**Output** (Methods, Data, p. 2):

> total stem was defined as groundline to tree tip

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-output

**Equation** (Methods, Model development, p. 2):

> k is a set segmentation point that is 9.0 inches for softwoods (SPCD<300) and 11.0 inches for hardwoods (SPCD≥300)

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-expression-2

**Fit** (Table S19_component_division_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,DIVISION,DIVISION_DESCRIPTION,N,Avg_DBH,Min_DBH,Max_DBH):

> "Total Stem Wood Volume","ST_WD_CV_TOT","202","M310","TROPICAL_SUBTROPICAL_STEPPE_REGIME_MOUNTAINS",339,17.2616519174041,1,44.8

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-fit

**Fit** (Methods, Model development, p. 6):

> key modeling statistics such as sample sizes (n), tree diameter distributions (minimum, mean, and maximum)

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#quote-fit-2

**Our note:** Output is gross total stem wood volume inside bark, groundline to tip (VtotibGross), before cull or broken-top deductions. DBH is measured at 4.5 ft (1.37 m). Paper units: in, ft, ft3; expression converts D cm→in (/2.54), H m→ft (/0.3048) and ft3→m3 (×0.028316846592). n and the DBH range are from the scorecard for ST_WD_CV_TOT in M310 (table S19) and cover the whole segmented model; the record's DBH limit at k is the segmentation point. Lower branch of the segmented model; pair with westfall-2024-pseudotsuga-menziesii-m310-volume-large.

## Checks this equation passes

On every build, the library's form and the source's own form (in its units) must both give these values within 1%.

| Inputs | Expected | We get | From |
| --- | --- | --- | --- |
| D = 15.24, H = 13.716 | 0.101 | 0.101 | Computed from the printed form: computed from the published form at D = 6 in, H = 45 ft, converted to cm, m and m3 |

Cite: https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/#checks

## How to cite

Cite the source for the equation: Westfall, J.A., Coulston, J.W., Gray, A.N., Shaw, J.D., Radtke, P.J., Walker, D.M., Weiskittel, A.R., et al. (2024). A national-scale tree volume, biomass, and carbon modeling system for the United States. Gen. Tech. Rep. WO-104. Washington, DC: USDA Forest Service. 37 p. https://doi.org/10.2737/WO-GTR-104

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "NSVB Douglas-fir, Tropical Subtropical Steppe Regime Mountains (M310): total stem wood volume (inside bark), segmented model (Eq. 2), D < 9 in (22.86 cm)", checked 2026-11-03, https://treeallometry.org/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small/. Data CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Quotes are the authors' words.

Data for this equation: https://treeallometry.org/data/equations/westfall-2024-pseudotsuga-menziesii-m310-volume-small.json
Report a problem: email info@restorationscope.com with the equation id (westfall-2024-pseudotsuga-menziesii-m310-volume-small) and where the right value appears.